Obligatory "Not an actual historian, just basing an answer off of what I know"...
I would say the middle to end of May, 1941.
England has pushed back (the brunt of) the German attacks on Britain (the Blitz has ended, but raids are still happening at a reduced rate), but things aren't going well in the rest of the world. England is making some headway in Africa, but they also have to fight a new Nazi-sympathetic regime in Iraq - Fuhrer Directive No. 30 said that "The Arab Freedom Movement in the Middle East" was Germany's "natural ally against England", so there were an awful lot of possible insurrections and rebellions that needed to be dealt with. In addition, it was in May 1941 that England began to evacuate and eventually lost Crete, meaning that Germany had cemented its hold over the Mediterranean - at the end of April, Greece had surrendered to Germany, so there really wasn't any opposition left.
Inside Germany, May saw the Strike of the 100,000. Somewhere around 70,000 workers in Belgium and Flanders went on strike, partly for increased wages, partly to protest the German occupation. The Nazi party was concerned that something like that could happen again, and would arrest 400 people in September 1942 for supposedly planning another strike. They obviously understood that people didn't exactly like living in an occupation, so it would be easy enough to imagine an alternate history where Germany offered peace so that they could stabilize their new population.
The other big thing is that in late May, a German U-boat sunk the US merchantman SS Robin Moor. While it didn't have as much of an effect on the US population as the sinking of the Lusitania did in WWI, it certainly solidified the Roosevelt Administration's dislike of Germany. Shortly after the sinking, German assets in the US were frozen and the State Department asked Germany and Italy to remove all consulates from US soil except the main embassies. While the US was already sending aid to England and China due to the Lend-Lease Bill, the sinking of Robin Moor made them dislike Germany even more.
If we look at it all through a certain lens, we can see England fighting on its own (plus some aid from the US) against a Germany that is gaining ground all across Europe and getting new allies in Middle Eastern rebels it supports, but facing internal strife from all the land it's occupying. The USSR is still allied with Germany until June 22 (Barbarossa). I can see a German offer of peace being successful at that point, since the US is still unwilling to truly join the war and England has just been hit with a string of defeats.